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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>(<dfn class="terminology">Case 1)</dfn> <span class="process-math">\(g(x)=P_m(x)=b_0 x^m+b_1 x^{m-1}+\cdots+b_m\text{.}\)</span>(1 a) <span class="process-math">\(a_n \neq 0\text{:}\)</span> Form of the particular solution:</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
Y=A_0 x^m+A_1 x^{m-1}+\cdots+A_m.
\end{equation*}
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<p class="continuation">(1 b) <span class="process-math">\(a_n=a_{n-1}=\cdots=a_{n-s}=0\)</span> (there are <span class="process-math">\(s+1\)</span> lower order coefficients equal to zero) which implies <span class="process-math">\(x, x^2, \cdots, x^s\)</span> are solutions to the homogeneous equation. Then the form of the particular solution is</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
Y=x^{s+1} (A_0 x^m+A_1 x^{m-1}+\cdots+A_m).
\end{equation*}
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